I don't mind playing support, I actually enjoy it most of the times. My question then is, in saying that one of my Summoner spells is already Flash for both situations, when should I use Clairvoyance and when should I use Heal?
If you are solo queing, don't ever pick CV. Your team simply doesn't have the map awareness, or coordination to take advantage of the power of CV. CV is strong when your team can use it to find out where people are and kill them. In a solo que game, most of your teammates are busy doing there own thing and complaining because you didn't call MIA. Pick up heal then, to help your lane survive a little bit more. Its a good pick even on champions that do have heal (Soraka with heal + summoner heal + ultimate is hard as fuck to take down).
In most games, the AD carry should be running heal. This is because it benefits them much more because when you are away, they still have a "heal bait" ability. And if you ever get zones away from them, they still have more survivability. Instead you should pick up exhust most of the time, because it extends the control you have over the game. An exhuast on kennen the second he ult can win you a team fight instead of getting your team aced. Plus, exhaust with its constant slow and damage reduction will help a lot more if you get caught while you are trying to save a ward.
I usually try to use Heal on champions that don't have a good heal built-in, such as Lulu or Orianna. Clairvoyance is good when you can reveal an enemy for your team, such as for a Nocturne or Karthus ultimate.
It usually depends on the champions on each team. If you have a strong mid lane and jungle, going Clairvoyance to help with counterjungling would be a good idea. If you are have a bot lane that is probably going to lose, heal is a better choice to help in fights. Also using Clairvoyance can be helpful if you have a lane you know you are going to win as you can use it to help stop ganks.
Along with what Ace said about running heals on champions that don't have good heal abilities, when you're running CV, make sure to start off the game by casting it on the enemy summoner platform. If you time it right, this will allow you to not only see the enemy starting builds, but also who's going where, etc.
In the current Meta it's never worth it to run CV unless you are talking to your Jungler on skype or in an organized game with other people. It relies ENTIRELY on your team being aware of when and where you use it and for gaining specific information on where the jungler is at any given time.
The best bet for bottom is actually to run Exhaust and Flash, where as the AD carry runs Heal/flash or cleanse/flash. You can also run Double heal bottom lane with both the AD and support getting it but in general i tend to only do this on games where i'm against a "kill lane" (IE ali trist, ali vayne, nunu/graves) where the lane is constant hyper aggressive. Just by LIVING in these lanes you can "win" the lane, and thus it's not so much about aggression as sustain.
Heal is a better ability to get on the AD for a variety of reasons, the most important being that it is 100% effective on them and thus maximizes the potential for it's use on an AD carry. It also tends to heal for more than when on a support, where as it doesnt matter who uses exhaust.